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A144552 Triangular numbers n*(n+1)/2 such that the three numbers n, n+1 and A001222(n) + A001222(n+1) are all composite. 2

%I #10 Jun 05 2017 14:17:16

%S 45,105,120,231,300,325,378,561,595,630,741,780,990,1485,1540,1596,

%T 1653,2016,2080,2850,3240,3321,3570,3655,3741,3828,4095,4371,4465,

%U 4560,4851,6786,7021,7381,7503,7750,8256,8778,8911,9045,9180,9870,10011,10153

%N Triangular numbers n*(n+1)/2 such that the three numbers n, n+1 and A001222(n) + A001222(n+1) are all composite.

%H Harvey P. Dale, <a href="/A144552/b144552.txt">Table of n, a(n) for n = 1..2000</a>

%p A001222 := proc(n) numtheory[bigomega](n) ; end: isA144552 := proc(n) if A001222(n) <= 1 or A001222(n+1) <= 1 then RETURN(false) ; fi; if not isprime(A001222(n)+A001222(n+1)) then true; else false; fi; end: for n from 0 to 200 do if isA144552(n) then printf("%d,",n*(n+1)/2) ; fi; od: # _R. J. Mathar_, Jan 03 2009

%t Times@@#/2&/@Select[Partition[Select[Range[200],CompositeQ],2,1],#[[2]]- #[[1]] == 1&&CompositeQ[Total[PrimeOmega[#]]]&] (* _Harvey P. Dale_, Jun 05 2017 *)

%Y Cf. A002808, A141468. See A144581 for another version.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Dec 31 2008

%E Edited (and 1596 inserted) by _R. J. Mathar_, Jan 03 2009

%E Edited by _N. J. A. Sloane_, Jan 08 2009

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)